Seeing the video unfortunately doesn't give me a clue about the problem you're having. So I would need to see your SVG file. I have a couple of guesses, so I'll mention those. But if they don't seem to fit, we would need the SVG file.
The first thought is that you might have accidentally drawn the lines with the Pen tool in the wrong mode, or with a Shape option enabled. Or the other thought is that the Paint Bucket tool might have been on top of a line, instead of on top of the open area between the lines, at the moment when you clicked.
The reason I said that I would not use the Paint Bucket tool for any file that's going to be used with a digital cutter, such as Cricut, is because that tool is not just putting color in the area. It's also making a new path. So for each shape, you have more than one path associated with each area. I didn't watch the whole video, so maybe the author has some other steps to prevent the machine from "seeing" the wrong path (and cutting the wrong path).
Unfortunately, the alternative would require much more work, because the alternative means that you have to make a closed shape with each black line. I wrote a tutorial explaining how to do that, using the Node tool for editing. It's about editing a map, but it's essentially the same thing as what you're doing.
https://forum.inkscapecommunity.com/index.php?action=articles;sa=view;article=47However, I suppose that with stained glass, and how you cut the glass pieces, you can never attain the precision which the traditional fill technique would provide. So the generality associated with the Paint Bucket tool is probably an insignificant problem....or not any problem at all, really. I imagine that if your line if "off" by a pixel or 2, or maybe even a quarter of an inch, you can fill it in with....whatever goes in between the glass pieces (I'm sure it's not lead anymore).
Sigh, I've always wanted to try making stained glass as a hobby. I think it would be loads of fun! Unfortunately, at this point I'm fairly invested in maintaining this forum, and in participating in the Inkscape community. I'd have to give up this, to have enough time for that. But I really would love to do it!!
Actually, I've made loads of abstract geometric patterns, which I've created for people who like coloring (
https://inkscapecommunity.com/ic_gallery/index.php?cat=8) (and also some quilt patterns). I might have to adopt the perspective for stained glass patterns, and make some more new ones. I haven't gotten into mandalas at all, which I'm planning at some point. So that will be fun (whether anyone ever downloads one or not, haha!)!